Computational Complexity and other fun stuff in math and computer science from Lance Fortnow and Bill Gasarch

Thursday, June 01, 2006

Research with Colleagues Visiting for a Short Time

Another guest post by Bill Gasarch

A colleague is
going to visit for a short time and you want to get some research
done. When does this work? When does this not work? How to you define
`work' anyway? Some advice.

Have a well defined topic that at least one of you is knowledgeable about.

Have complimentary strengths. Or, more accurately, make sure that several
strengths are covered (e.g., one knows Algebra, one knows Geometry, so
you can do research in Algebraic Geometry. Well, maybe not...)
(Better example: one is a knowledgeable about widgets, and one is
clever with widgets.)

Don't chit-chat or socialize that much, OR
at least have it be during a well defined time. For example AT SCHOOL
mostly talk about research. AT HOME (if the visitor is staying at
your house) socialize. For this reason, having the visitor at your
house is a good idea so long as it makes sense logistically and is
okay with the spouse.

Avoid long big lunches. You feel sluggish afterwards.

Right after you've proven something new you are excited about it.
Write it up SOON, while you are still excited.
For work with visiting colleagues, make sure that ONE of you
is assigned to get out the first draft. (This is true of research in general.)

How long to stay? Too long can be bad since then there is the temptation
to put things off. About a week is good. If someone is visiting for a semester
than this is a whole different story, which someone else may blog on.

One goal of a collaboration working is that a paper is produced.
Other goals could be that you both learn something you didn't know before.

6 comments:

I just finished one week of collaboration with a visiting colleague. I could not agree more, maybe except with point 7. Usually the paper is still not written by the last day of the visit. I think that a draft is enough, as collaboration on the redaction can be done through email, at a slower pace.

Although, if having agreed on a topic from the begining is better, the complementarity is more important and usually suggests one (or more) topics, in the intersection of the expertise domains.

In systems one has to spend many long hours writing code to have a substantial result. In theory all it takes is a dip in the bathtub for that Eureka moment to hit you, and yes, here we are, talking about Archimedes' "substantial scientific result" overr 2000 years later.

This might indicate a fundamental problem in theoretical computer science.

News at 11: "Fundamental problem in TCS. It has fruitful and exciting collaborations!"

Theory and Eureka moments. In theory, a theory paper only needs an Eureka moment. In practice, any serious contribution to theory these days needs several Eureka moments (maybe a few on the technical side), and probably a few months of fruitless thinking.

Gettting two people in the same room certainly does not double the chances of an Eureka moment (some would say it doesn't even increase them). That's why you should expect that you will not make any significant progress on a major problem during a research visit.

Why have research visits at all? A very wrong goal for a research visit is to get a publication out of it. This leads to people working on problems where there's a reasonable expectation something will be done in a week. This in turn leads to countless mediocre papers polluting the field.

A better goal, in my opinion, is to exchange partial ideas / observations about important open problems. Do not expect the other person to have an immediate brilliant idea that will complete yours, but maybe he gets motivated enough to think about it later.

Of course, this requires a lot of trust in the other person's scientific and coauthorship ethics. It also requires good ethics on your side: if you get somebody interested in a problem and he solves it (maybe ignoring your suggestions), this doesn't automatically make you an author.

So I guess the summary is that a research visit is a mostly social event, just in a very technical context.

In practice, any serious contribution to theory these days needs several Eureka moments (maybe a few on the technical side), and probably a few months of fruitless thinking.

Research visits do not happen in the vacuum. One doesn't get together with a random person and go "lezzee what do we work on this week?"

A good research visit is either to a long standing collaborator or, in the case of a new researchers to someone chosen carefully for their similarity of interests. Then the problem one works on is one that at least one of the parties has spent a lot of time pondering and has even made partial progress. During the week long visit there might be one two or three insight moments (some more minor than others) and then after the visit there is a wrap up stage in which the last quirks and details are worked at a distance.

I disagree that nowadays strong papers need several Eureka moments. Most papers out there have one perhaps two real deep insights, and the rest is (admittedly non-trivial) mathematical development.

Such attitude evidences ignorance of the incremental nature of science. For every major paper out there fourty other "polluting papers" had to be published. Papers which hinted at the problem, reduced the space of solutions, showed the wrong way to go about it, and gave us insight as to where the difficulties lie.